A circle has a circumference of 31.4 meters. What is its radius?
["How to Calculate the Radius of a Circle with a Known Circumference – A Simple Guide", "When studying circles in math or geometry, one of the most basic yet essential questions is: What is the radius of a circle if its circumference is 31.4 meters? Understanding how to derive this measurement involves a key formula that connects circumference and radius — and solving this problem is a great way to practice applied geometry.", "### The Formula That Connects Circumference and Radius", "The circumference ( C ) of a circle is calculated using the formula:", "[\nC = 2\pi r\n]", "Where:\n- ( C ) is the circumference\n- ( \pi ) (pi) is approximately 3.14\n- ( r ) is the radius of the circle", "In this problem, we’re given that the circumference is ( C = 31.4 ) meters. We can substitute this value into the formula:", "[\n31.4 = 2 \ imes \pi \ imes r\n]", "### Solving for the Radius", "To find the radius ( r ), rearrange the formula:", "[\nr = \frac{C}{2\pi}\n]", "Substitute ( C = 31.4 ) and ( \pi \approx 3.14 ):", "[\nr = \frac{31.4}{2 \ imes 3.14} = \frac{31.4}{6.28} \approx 5\n]", "So, the radius of the circle is 5 meters.", "### Why This Matters: Practical Applications", "Knowing how to calculate the radius from the circumference is useful in many real-world scenarios, including:", "- Designing circular tracks, drums, or pipes\n- Planning landscaping projects like circular flower beds\n- Engineers calculating material needs for cylindrical structures\n- Physics and architecture involving rotational symmetry", "### Final Answer", "If a circle has a circumference of 31.4 meters, its radius is exactly 5 meters.", "This simple calculation reinforces the foundational relationship between a circle’s circumference and radius — a concept that underpins much more advanced geometry and trigonometry.", "Tip: If you prefer exact values, using ( \pi \approx \frac{22}{7} ) gives:", "[\nr = \frac{31.4}{2 \ imes \frac{22}{7}} = \frac{31.4 \ imes 7}{2 \ imes 22} = \frac{219.8}{44} = 5\n]", "Confirming again, the radius is 5 meters — consistent and accurate.", "---", "master the circle formula effortlessly and tackle related geometry problems with confidence!"]
